Vito Prosciutto: Teaching community college math on the road to a PhD.

Friday, August 22, 2003

Brain Rot 

I've decided to start moving my math teaching book mark list over to this log, and I'll put an entry in the log for each bookmark as they come. The first entry I'm moving over is an essay by Mathematica programmers Theodore Gray and Jerry Glyn, Will Mathematica rot students' brains. (As an aside, I discovered this essay courtesy of a friend pointing me at the story of Theodore's Sodium party and the rest of his site is well worth investigating for anyone who is intrigued by, well, anything vaguely scientific I suppose.)

This is the essay which completely turned me around on calculators in the classroom (although my experiences as a TA confirmed me in this metanoia). I think that the most blatant example of how calculators have changed the math curriculum even in my day is the lack of instruction in calculating square roots by hand. This used to be considered an essential skill, but while it was in my high school algebra text, it wasn't taught.

To a certain extent we're undergoing a more dramatic sea change in today's math world where calculators (particularly graphing calculators) make it possible to do mathematical tasks that would have been much more complicated before. A few button presses to calculate a definite integral, etc. I think that we're on the cusp of redefining mathematics education, although the politicians and the demagogues continue to have their say, unfortunately.

The impact of calculators and computers at the high school and college level is simple enough. It's now possible for students in a precalculus class, for example, to tackle questions of complicated definite integrals with minimal effort (although some of the examples of doing this seemed inordinately convoluted).

At the elementary level, things are a lot more complicated. Is it really necessary to do the kinds of arithmetic drills that were common when I was a child? I'm not sure. Theodore and Jerry find value in addition, but to me, long division is where it's at. After all, there's a whole world of mathematical discovery lurking in long division (starting with polynomial division, moving on to the Euclidean algorithim and thence to a whole world of number theory and discrete mathematics to touch just the tip of the iceberg). On the flip side, this is not the level of mathematical exploration that will be demanded of most of our students. As I've found, an inability to multiply 18 by 8 without a calculator does not necessarily imply that a student will not be able to master algebra (or at least grasp the concepts well enough to average 70% or above on tests and quizzes).

There's another side of this which is another important question to address: The use of technology in the classroom can open a divide between those who have the resources to obtain the technology and those who don't. Consider, for example, that while a basic supermarket calculator will run only $5-10, with basic statistics available for under $20, graphing calculators come in at $60-100 or more. Mathematica for students is $140, and the compute that can run it will be at least $500. That's an awful big bite if you're trying to raise a family on minimum wage.

I'd love to hear comments from any readers of this blog (or acknowledgment of the existence of any readers of this blog).

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